A blockchain exists out of blocks of data. These blocks of data are stored on nodes (compare it to small servers). Nodes can be any kind of device (mostly computers, laptops or even bigger servers). Nodes form the infrastructure of a blockchain.
All nodes on a blockchain are connected to each other and they constantly exchange the latest blockchain data with each other so all nodes stay up to date. They store, spread and preserve the blockchain data, so theoretically a blockchain exists on nodes.
A full node is basically a device (like a computer) that contains a full copy of the transaction history of the blockchain.
